Two-loop superstrings and S-duality

TL;DR

This paper compares two-loop superstring calculations with duality predictions for the $D^4 R^4$ term in Type IIB string theory, confirming the SL(2,Z) duality conjecture through precise normalization and factorization techniques.

Contribution

It provides an exact match between superstring perturbation results and duality predictions for the two-loop $D^4 R^4$ term, validating the SL(2,Z) duality in Type IIB string theory.

Findings

Two-loop superstring contributions match duality predictions.

Normalization of the 4-point function is precisely determined.

The $D^2F^4$ term in heterotic theory is evaluated, but its duality significance remains open.

Abstract

The two-loop contribution to the Type IIB low energy effective action term $D^4 R^4$, predicted by SL(2,Z) duality, is compared with that of the two-loop 4-point function derived recently in superstring perturbation theory through the method of projection onto super period matrices. For this, the precise overall normalization of the 4-point function is determined through factorization. The resulting contributions to $D^4 R^4$ match exactly, thus providing an indirect check of SL(2,Z) duality. The two-loop Heterotic low energy term $D^2F^4$ is evaluated in string perturbation theory; its form is closely related to the $D^4 R^4$ term in Type II, although its significance to duality is an open issue.